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A multiplicative dual of nil-clean rings

Part of: Rings and algebras arising under various constructions Conditions on elements Local rings and generalizations

Published online by Cambridge University Press:  09 February 2021

Yiqiang Zhou
Yiqiang Zhou*
Affiliation:
Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John’s, NLA1C 5S7, Canada
*
e-mail: zhou@mun.ca
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Abstract

The goal of this note is to completely determine the rings for which every nonunit is a product of a nilpotent and an idempotent (in either order).

Keywords

Idempotentnilpotentnil-clean ringdual nil-clean ring

MSC classification

Primary: 16U99: None of the above, but in this section
Secondary: 16L30: Noncommutative local and semilocal rings, perfect rings 16S50: Endomorphism rings; matrix rings
Type
Article
Information
Canadian Mathematical Bulletin , Volume 65 , Issue 1 , March 2022 , pp. 39 - 43
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Copyright
© Canadian Mathematical Society 2021

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